why is steam commonly used in ironing polyester and cotton fabrics?

Answer 1

because the steam makes the fibres wet, which makes cotton fibres more smooth and polyester more flexible, so they can slide agaisnt each other more easily, which helps in flattening out creases in the fabric

Answer 2

Most important use is for polyester. This fiber has a very low melting point. Even though steam is at a high temperature, it can be diminished by application from a proper distance, and the fact that heat is not directly applied to the fiber, as an iron would do.

Cottons tend to wrinkle very easily and steam is much easier to use on an oft-needed basis. It can also be more readily applied to a single wrinkle or two without "ironing" the entire garment.